- #1
cmajor47
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Homework Statement
Use the method of separation of variables or an integrating factor to find a particular solution of the differential equation that satisfies the given initial condition.
y'=x-y+2 ; y(0)=4
2. The attempt at a solution
I've used an integrating factor of e[itex]^{x}[/itex] to obtain the following from y'=x-y+2:
[itex]\frac{d}{dx}[/itex]e[itex]^{x}[/itex]y=xe[itex]^{x}[/itex]+2e[itex]^{x}[/itex]
I know that I know have to integrate both sides of the equation. However, this is an issue since the equation contains the term xe[itex]^{x}[/itex]. This book hasn't yet taught integration by parts which is commonly used to integrate xe[itex]^{x}[/itex]. I don't think that separation of variables can be used to solve integrate this either.
Therefore, my question is: is there a way to integrate xe[itex]^{x}[/itex] without using integration by parts?